Dynamics of quadratic polynomial mappings of C2

extensions of some polynomial inequalities to the polar derivative

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Stability of Approximate Quadratic Mappings

In 1940, Ulam 1 gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems. Among these was the following question concerning the stability of homomorphisms. Let G1 be a group and let G2 be a metric group with metric ρ ·, · . Given > 0, does there exist a δ > 0 such that if f : G1 → G2 satisfies ρ f xy , f x f y < δ for all x, y ∈ ...

Relative cohomology of polynomial mappings

Let F be a polynomial mapping from C to C with n > q. We study the De Rham cohomology of its fibres and its relative cohomology groups, by introducing a special fibre F−1(∞) ”at infinity” and its cohomology. Let us fix a weighted homogeneous degree on C[x1, ..., xn] with strictly positive weights. The fibre at infinity is the zero set of the leading terms of the coordinate functions of F . We i...

Multivariate Nonnegative Quadratic Mappings

In this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity defined by a pre-specified conic order. In particular, we consider the set (cone) of nonnegative quadratic mappings defined with respect to the positive semidefinite matrix cone, and study when it can be represe...

Generalized Stability of C∗-Ternary Quadratic Mappings